Is a loss function the flip side of a coin to a utility function, or are they not related? I'm trying to get a grasp on utility and loss functions, and at first I thought that a utility function was the flipside of a loss function and vice versa. Kind of like how if you know the probability of getting heads is p, you know the probability of getting tails (1-p). However, I can't find anything on the internet to that effect. I might be thinking of the regret function, but I'm not sure. Am I missing something?   
 A: $U(x)=-\mathcal{L}(x)$.  I cannot imagine you will find anything on the internet.  I believe you can find a formal treatment of these functions in Geweke's "Contemporary Bayesian Econometrics and Statistics."
A: Loss is a negative utility. If you need an authoritative source for this, check the Statistical Decision Theory book by James O. Berger (p. 53):

Once $U(\theta, a)$ has been obtained, the loss function can simply be
  defined as
$$ L(\theta, a) = -U(\theta, a). \tag{2.3} $$

The same is stated by Christian P. Robert in his book The Bayesian Choice, who introduces utility with the following notion (p. 54):

The notion of utility (defined as the opposite of loss) is used not
  only in Statistics, but also in Economics and in other fields like
  Game Theory where it is necessary to order consequences of actions or
  decisions. Consequences (or rewards) are generic notions which
  summarize the set of outcomes resulting from the decision-maker’s
  action. In the simplest cases, it may be the monetary profit or loss
  resulting from the decision. (...)

